Question

a square+1/a square= 2 then a+
1/a​

Answer 1

Answer:

Recalling the formulae ,

(a+b)2=(a−b)2+4ab(a+b)2=(a−b)2+4ab

Using the above formulae in the given question,

(a+1/a)2=(a−1/a)2+4a.(1/a)(a+1/a)2=(a−1/a)2+4a.(1/a)

=(a−1/a)2+4=(a−1/a)2+4

Now, (a−1/a)2+4−2(a−1/a)=12(a−1/a)2+4−2(a−1/a)=12

Let(a−1/a)=z.(a−1/a)=z.

=z2−2z+4−12=0=z2−2z+4−12=0

=z2−2z−8=0=z2−2z−8=0

=z2−(4−2)z−8=0z2−(4−2)z−8=0

= z2−4z+2z−8=0z2−4z+2z−8=0

=z(z−4)+2(z−4)=0z(z−4)+2(z−4)=0

=(z−4)(z+2)=0(z−4)(z+2)=0

Eitherz=4orz=−2z=4orz=−2

Either

Explanation:

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